analyze the function for domain, range, continuity, increasing or decreasing behavior, symmetry…

analyze the function for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior. f(x)=tan^(-1)x a. the function has one horizontal asymptote at. (type an equation. simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the equation.) b. the function has two horizontal asymptotes. the top asymptote is y = π/2 and the bottom asymptote is y = -π/2 (type equations. simplify your answers. type exact answers, using π as needed. use integers or fractions for any numbers in the equations.) c. the function has no horizontal asymptotes. identify any vertical asymptotes. select the correct choice and, if necessary, fill in the answer box to complete your choice. a. the function has two vertical asymptotes. the leftmost asymptote is and the rightmost asymptote is (type equations. simplify your answers. type exact answers, using π as needed. use integers or fractions for any numbers in the equations.) b. the function has one vertical asymptote at. (type an equation. simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the equation.) c. the function has no vertical asymptotes

analyze the function for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior. f(x)=tan^(-1)x a. the function has one horizontal asymptote at. (type an equation. simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the equation.) b. the function has two horizontal asymptotes. the top asymptote is y = π/2 and the bottom asymptote is y = -π/2 (type equations. simplify your answers. type exact answers, using π as needed. use integers or fractions for any numbers in the equations.) c. the function has no horizontal asymptotes. identify any vertical asymptotes. select the correct choice and, if necessary, fill in the answer box to complete your choice. a. the function has two vertical asymptotes. the leftmost asymptote is and the rightmost asymptote is (type equations. simplify your answers. type exact answers, using π as needed. use integers or fractions for any numbers in the equations.) b. the function has one vertical asymptote at. (type an equation. simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the equation.) c. the function has no vertical asymptotes

Answer

Answer:

  1. B. The function has two horizontal asymptotes. The top asymptote is $y = \frac{\pi}{2}$ and the bottom asymptote is $y=-\frac{\pi}{2}$
  2. C. The function has no vertical asymptotes

Explanation:

Step1: Recall arctangent properties

The function $y = \tan^{- 1}(x)$ is the inverse - tangent function.

Step2: Determine horizontal asymptotes

As $x\to+\infty$, $\lim_{x\to+\infty}\tan^{-1}(x)=\frac{\pi}{2}$. As $x\to-\infty$, $\lim_{x\to-\infty}\tan^{-1}(x)=-\frac{\pi}{2}$. So, it has two horizontal asymptotes $y = \frac{\pi}{2}$ and $y =-\frac{\pi}{2}$.

Step3: Determine vertical asymptotes

The domain of $y=\tan^{-1}(x)$ is $(-\infty,\infty)$. Since the function is defined for all real - valued $x$, there are no vertical asymptotes.